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. 1999 Sep;77(3):1316–1326. doi: 10.1016/S0006-3495(99)76981-X

A polarization model overcoming the geometric restrictions of the laplace solution for spheroidal cells: obtaining new equations for field-induced forces and transmembrane potential.

J Gimsa 1, D Wachner 1
PMCID: PMC1300421  PMID: 10465744

Abstract

We present a new model for a variety of electric polarization effects on oblate and prolate homogeneous and single-shell spheroids. For homogeneous spheroids the model is identical to the Laplace model. For single-shell spheres of cell-like geometry the calculated difference of the induced dipole moments is in the thousandths range. To solve Laplace's equation for nonspherical single-shell objects it is necessary to assume a confocal shell, which results in different cell membrane properties in the pole and equator regions, respectively. Our alternative model addresses this drawback. It assumes that the disturbance of the external field due to polarization may project into the medium to a characteristic distance, the influential radius. This parameter is related to the axis ratio of the spheroid over the depolarizing factors and allows us to determine the geometry for a finite resistor-capacitor model. From this model the potential at the spheroid's surface is obtained and, consequently, the local field inside a homogeneous spheroid is determined. In the single-shell case, this is the effective local field of an equivalent homogeneous spheroid. Finally, integration over the volume yields the frequency-dependent induced dipole moment. The resistor-capacitor approach allowed us to find simple equations for the critical and characteristic frequencies, force plateaus and peak heights of deformation, dielectrophoresis and electrorotation for homogeneous and single-shell spheroids, and a more generalized equation for the induced transmembrane potential of spheroidal cells.

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Selected References

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  1. Archer G. P., Betts W. B., Haigh T. Rapid differentiation of untreated, autoclaved and ozone-treated Cryptosporidium parvum oocysts using dielectrophoresis. Microbios. 1993;73(296):165–172. [PubMed] [Google Scholar]
  2. Asbury C. L., van den Engh G. Trapping of DNA in nonuniform oscillating electric fields. Biophys J. 1998 Feb;74(2 Pt 1):1024–1030. doi: 10.1016/s0006-3495(98)74027-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Becker F. F., Wang X. B., Huang Y., Pethig R., Vykoukal J., Gascoyne P. R. Separation of human breast cancer cells from blood by differential dielectric affinity. Proc Natl Acad Sci U S A. 1995 Jan 31;92(3):860–864. doi: 10.1073/pnas.92.3.860. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Fuhr G., Müller T., Baukloh V., Lucas K. High-frequency electric field trapping of individual human spermatozoa. Hum Reprod. 1998 Jan;13(1):136–141. doi: 10.1093/humrep/13.1.136. [DOI] [PubMed] [Google Scholar]
  5. Georgieva R., Neu B., Shilov V. M., Knippel E., Budde A., Latza R., Donath E., Kiesewetter H., Bäumler H. Low frequency electrorotation of fixed red blood cells. Biophys J. 1998 Apr;74(4):2114–2120. doi: 10.1016/S0006-3495(98)77918-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Gimsa J., Eppmann P., Prüger B. Introducing phase analysis light scattering for dielectric characterization: measurement of traveling-wave pumping. Biophys J. 1997 Dec;73(6):3309–3316. doi: 10.1016/S0006-3495(97)78355-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Gimsa J., Müller T., Schnelle T., Fuhr G. Dielectric spectroscopy of single human erythrocytes at physiological ionic strength: dispersion of the cytoplasm. Biophys J. 1996 Jul;71(1):495–506. doi: 10.1016/S0006-3495(96)79251-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Gimsa J., Wachner D. A unified resistor-capacitor model for impedance, dielectrophoresis, electrorotation, and induced transmembrane potential. Biophys J. 1998 Aug;75(2):1107–1116. doi: 10.1016/S0006-3495(98)77600-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Grosse C., Schwan H. P. Cellular membrane potentials induced by alternating fields. Biophys J. 1992 Dec;63(6):1632–1642. doi: 10.1016/S0006-3495(92)81740-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hagedorn R., Fuhr G., Müller T., Gimsa J. Traveling-wave dielectrophoresis of microparticles. Electrophoresis. 1992 Jan-Feb;13(1-2):49–54. doi: 10.1002/elps.1150130110. [DOI] [PubMed] [Google Scholar]
  11. Hölzel R. Electrorotation of single yeast cells at frequencies between 100 Hz and 1.6 GHz. Biophys J. 1997 Aug;73(2):1103–1109. doi: 10.1016/S0006-3495(97)78142-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Hölzel R. Nystatin-induced changes in yeast monitored by time-resolved automated single cell electrorotation. Biochim Biophys Acta. 1998 Oct 23;1425(2):311–318. doi: 10.1016/s0304-4165(98)00083-x. [DOI] [PubMed] [Google Scholar]
  13. Kinosita K., Jr, Tsong T. Y. Voltage-induced pore formation and hemolysis of human erythrocytes. Biochim Biophys Acta. 1977 Dec 1;471(2):227–242. doi: 10.1016/0005-2736(77)90252-8. [DOI] [PubMed] [Google Scholar]
  14. Krueger M., Thom F. Deformability and stability of erythrocytes in high-frequency electric fields down to subzero temperatures. Biophys J. 1997 Nov;73(5):2653–2666. doi: 10.1016/S0006-3495(97)78294-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Maier H. Electrorotation of colloidal particles and cells depends on surface charge. Biophys J. 1997 Sep;73(3):1617–1626. doi: 10.1016/S0006-3495(97)78193-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Miller R. D., Jones T. B. Electro-orientation of ellipsoidal erythrocytes. Theory and experiment. Biophys J. 1993 May;64(5):1588–1595. doi: 10.1016/S0006-3495(93)81529-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. PAULY H., SCHWAN H. P. Uber die Impedanz einer Suspension von kugelförmigen Teilchen mit einer Schale; Ein Modell fur das dielektrische Verhalten von Zellsuspensionen und von Proteinlösungen. Z Naturforsch B. 1959 Feb;14B(2):125–131. [PubMed] [Google Scholar]
  18. Paul R., Otwinowski M. The theory of the frequency response of ellipsoidal biological cells in rotating electrical fields. J Theor Biol. 1991 Feb 21;148(4):495–519. doi: 10.1016/s0022-5193(05)80233-4. [DOI] [PubMed] [Google Scholar]
  19. Prüger B., Eppmann P., Donath E., Gimsa J. Measurement of inherent particle properties by dynamic light scattering: introducing electrorotational light scattering. Biophys J. 1997 Mar;72(3):1414–1424. doi: 10.1016/S0006-3495(97)78788-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Sukhorukov V. L., Mussauer H., Zimmermann U. The effect of electrical deformation forces on the electropermeabilization of erythrocyte membranes in low- and high-conductivity media. J Membr Biol. 1998 Jun 1;163(3):235–245. doi: 10.1007/s002329900387. [DOI] [PubMed] [Google Scholar]

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